Equilibrium Fluid Research Articles

The effect of supercritical fluids on Nb-Ta fractionation in subduction zones: Geochemical insights from a coesite-bearing eclogite-vein system

Supercritical fluids are ideal media for mass transfer from the subducting slab into the mantle wedge. However, little is known about the role of natural supercritical fluids in subduction zones. A combined study of petrology, geochemistry and zirconology was carried out for a coesite-bearing eclogitic vein and its surrounding eclogites from the Dabie orogen, one of the typical continental subduction zones on Earth. The results are used to reveal the composition and source of supercritical fluids, the P-T conditions and timing of their formation and their geochemical effects in subduction zones. The eclogitic vein is composed of garnet, omphacite, quartz, amphibole, rutile and apatite, with minor amounts of epidote, plagioclase and zircon. Coesite was identified in omphacite in the vein, demonstrating its formation under ultrahigh-pressure (UHP) metamorphic conditions that correspond to subarc depths in oceanic subduction zones. Zircons from the vein give concordant U-Pb ages of 225 ± 5 Ma and flat HREE patterns for newly grown rims, consistent with their crystallization at the UHP eclogite facies. The vein shows similar Hf-O isotope compositions to the host UHP eclogites, indicating that the UHP vein-forming fluid is internally buffered within the UHP eclogites. Minerals in the vein contain not only higher contents of Cr, Ni, Sr, REE and HFSE, but also multiphase crystal inclusions (such as omphacite, quartz, epidote, apatite, amphibole, plagioclase, mica, rutile, calcite, and anhydrite) as well as liquid and gas phases of H2O. The calculated fluid composition of major elements is 31 wt% SiO2, 20 wt% CaO, 10 wt% (SO4)2−, 8 wt% (CO3)2−, 8 wt% FeO, 7 wt% Al2O3, and 9 wt% H2O, with traces of Na2O, K2O and TiO2. This composition is responsible for the UHP veining from supercritical silicate-rich fluids in equilibrium with peak UHP minerals. The P-T-t path of the UHP eclogite-vein system indicates that the second critical endpoint of the basalt-H2O system is located close to 3.4 GPa and 770°C. The high contents of sulfate and carbonate in the vein suggest that supercritical fluids were oxidized and likely a predominant agent to transfer sulfur and carbon at subarc depths. High Nb/Ta ratios of rutile crystals in the vein and quantitative modelling indicate that dehydration of subducting eclogites at subarc depths can produce supercritical fluids with suprachondritic Nb/Ta ratios. The UHP eclogites and mantle wedge peridotites metasomatized by supercritical fluids can acquire suprachondritic Nb/Ta ratios and thus provide a complementary reservoir to balance the subchondritic reservoirs on Earth. Based on a statistics of Nb-Ta data, two indices are proposed to identify the existence of supercritical fluids in fossil subduction zones: (1) rutile crystallized from supercritical fluids shows lower Nb contents than that from aqueous solutions and hydrous melts; (2) UHP eclogites associated with supercritical fluids exhibit a distance >0.1 in their Nb-Ta compositions to the line defined by basalts in the plot of log[Nb] vs log[Ta]. Therefore, the existence of supercritical fluids during UHP metamorphism at subarc depths can be recognized from their effect on the mobility of fluid-immobile trace elements in UHP metamorphic rocks.

Hard-core attractive Yukawa fluid global isomorphism with the lattice gas model.

In this work, we study the global isomorphism between the liquid-vapor equilibrium of the hardcore attractive Yukawa fluid (HCAYF) and that of the Lattice Gas (LG) model of the Ising-like type. The applicability of the global isomorphism transformation and the dependence of its parameters on the screening length of the Yukawa potential are discussed. These parameters determine both the slope of the rectilinear diameter of the liquid-vapor binodal and the Zeno-element, which are the core ingredients of the fluid-LG isomorphism. We compare the Zeno-element parameters with the virial Zeno-line parameters, which are commonly used in the literature for the formulation of generalized law of the correspondent states. It is demonstrated that the Zeno-element parameters appear to be sensitive to the liquid state instability when the interaction potential becomes too short-ranged, while the virial ones do not show any peculiarities connected with this specific of the HCAYF.

Thermodynamic perfect fluid spheres admitting an orthogonal flat synchronization

We analyze the interpretation of the spherically symmetric perfect fluid solutions that admit a flat synchronization orthogonal to the fluid flow as a thermodynamic perfect fluid in local thermal equilibrium. The ideal gas sonic condition is examined for this family of metrics, and the macroscopic conditions for physical reality are accurately tested for some specific solutions.

Correlation of copeptin with osmolarity and electrolytes in diabetes Mellitus: A tertiary center outpatient experience.

Background: Arginine Vasopressin (AVP) plays a significant role in the pathophysiology of Diabetes Mellitus (DM) and its related nephropathy. Timely detection of copeptin, a surrogate biomarker of AVP, would help in minimizing the osmoregulatory complications secondary to DM. The study aimed to correlate serum copeptin levels with serum osmolarity and electrolytes in subjects with progressive stages of DM. Methodology: A total of 120 patients were recruited as controls, pre-diabetes, DM without nephropathy, and nephropathy. Serum copeptin levels were measured by Enzyme-Linked Immunosorbent Assay. At the same time, routine biochemical tests for diabetes and renal function were done from the affiliated diagnostic laboratory. Results: The mean copeptin and osmolarity levels were 207.74 ± 192.08 pg/ml and 302.29 ± 18.13 mOsm/kg, respectively. Both, the copeptin and osmolarity levels raises progressively from controls to various stages of DM and share significant positive correlation (r=0.214, p=0.019). Osmolarity was also correlated significantly with RBS (r=0.262), BUN (r=0.844), Na+ (r=0.210) and K+ (r=0.461). Conclusion: The significant correlation of copeptin with osmolarity highlights the importance of the AVP system in regulating body fluid equilibrium in diabetic patients progressing towards nephropathy. Timely detection of copeptin can play an important role in the early management of the disease.

Variation-Free Approach for Density Functional Theory: Data-Driven Stochastic Optimization

Density functional theory (DFT) is an efficient instrument for describing a wide range of nanoscale phenomena: wetting transition, capillary condensation, adsorption, etc. In this paper, we suggest a method for obtaining the equilibrium molecular fluid density in a nanopore using DFT without calculating the free-energy variation─Variation-Free Density Functional Theory (VF-DFT). This technique can be used to explore confined fluids with a complex type of interactions, additional constraints, and, to speed up calculations, which might be crucial in an inverse problem. The fluid density in VF-DFT approach is represented as a decomposition over a limited set of basis functions. We applied principal component analysis (PCA) to extract the basic patterns from the density function and take them into account in the construction of a set of basis functions. The decomposition coefficients of the fluid density by the basis were sought by stochastic optimization algorithms: genetic algorithm (GA) and particle swarm optimization (PSO), to minimize the free energy of the system. In this work, two different fluids were studied: nitrogen at a temperature of 77.4 K and argon 87.3 K, at a pore size of 3.6 nm, and the performance of optimization algorithms was compared. We also introduce the Hybrid Density Functional Theory (H-DFT) approach based on stochastic optimization methods and the classical Picard iteration method to find the equilibrium fluid density starting from the physically appropriate solution. The combination of Picard iteration and stochastic algorithms helps to significantly speed up the calculations of equilibrium density in the system without losing the quality of the solution, especially in cases with the high relative pressure and expressed layering structure.

Constraining Non-Dissipative Transport Coefficients in Global Equilibrium

The fluid in global equilibrium must fulfill some constraints. These constraints can be derived from quantum statistical theory or kinetic theory. In this work, we show how these constraints can be applied to determine the non-dissipative transport coefficients for chiral systems along with the energy-momentum conservation, chiral anomaly for charge current and trace anomaly in the energy-momentum tensor.

Local temperature in general relativity

We examine the Tolman temperature by using Carter's variational formalism of thermodynamics. We restrict our interests to fluids in thermal equilibrium that the heat does not propagate. We show that this condition presents a general formula for the local temperature gradient. We suggest a resolution of the recently addressed conflict in Tolman temperature when a chemical potential does not vanish.

Hydrodynamic correlation functions of chiral active fluids

The success of spectroscopy to characterise equilibrium fluids, for example the heat capacity ratio, suggests a parallel approach for active fluids. Here, we start from a hydrodynamic description of chiral active fluids composed of spinning constituents and derive their low-frequency, long-wavelength response functions using the Kadanoff-Martin formalism. We find that the presence of odd (equivalently, Hall) viscosity leads to mixed density-vorticity response even at linear order. Such response, prohibited in time-reversal-invariant fluids, is a large-scale manifestation of the microscopic breaking of time-reversal symmetry. Our work suggests possible experimental probes that can measure anomalous transport coefficients in active fluids through dynamic light scattering.

Thermodynamic equilibrium condition and the first law of thermodynamics for charged perfect fluids in electromagnetic and gravitational fields

We provide a proof of the necessary and sufficient condition on the profile of the temperature, chemical potential, and angular velocity for a charged perfect fluid in dynamic equilibrium to be in thermodynamic equilibrium not only in fixed but also in dynamical electromagnetic and gravitational fields. In passing, we also present the corresponding expression for the first law of thermodynamics for such a charged star.

A New Procedure For Reservoir Fluid Characterization With Equation Of State (EOS)

A new procedure for reservoir fluid characterization through equation of state (EOS) is proposed. It is applied in a selecting the most appropriate fluid composition for the purpose of reservoir fluid characterization. A Hoffman-Crump-Hocott plot is used to determine whether or not the streams are genuine equilibrium fluids. With the aid of phase diagram and saturation pressure from RFT, the most appropriate fluid sample was chosen for fitting an equation of state to experimental data through regression. Based on data analysis and quality control of all PVT data suggested that fluid from UP-1 DST-3 is the best representative of XYZ field. The PR3-EOS and LBC correlation are applied to the UP-1 DST-3 data sets under conditions of predictions and regression. Agreement between laboratory data and regressed EOS results is generally good to excellent. The results show that that regression on critical properties of components is sufficient for good data matches. In this work, a good agreement with experimental data was obtained with grouping (lumping) 15 to 7 components.

Steady asymptotic equilibria in conformal relativistic fluids

When one considers a shock wave in the frame where the shock is at rest, on either side one has a steady flow which converges to equilibrium away from the shock. However, hydrodynamics is unable to describe this flow if the asymptotic velocity is higher than the characteristic speed of the theory. We obtain an exact solution for the decay rate to equilibrium for a conformal fluid in kinetic theory under the relaxation time approximation, and compare it to two hydrodynamic schemes, one accounting for the second moments of the distribution function and thus equivalent, in the small deviations from equilibrium limit, to an Israel-Stewart framework, and another accounting for both second and third moments. While still having a finite characteristic speed, the second model is a significant improvement on the first.

Self-consistent relaxation theory of collective ion dynamics in Yukawa one-component plasmas under intermediate screening regimes.

The self-consistent relaxation theory is employed to describe the collective ion dynamics in strongly coupled Yukawa classical one-component plasmas. The theory is applied to equilibrium states corresponding to intermediate screening regimes with appropriate values of the structure and coupling parameters. The information about the structure (the radial distribution function and the static structure factor) and the thermodynamics of the system are sufficient to describe collective dynamics over a wide range of spatial scales, namely, from the extended hydrodynamic to the microscopic dynamics scale. The main experimentally measurable characteristics of the equilibrium collective dynamics of ions-the spectrum of the dynamic structure factor, the dispersion parameters, the speed of sound, and the sound attenuation-are determined within the framework of the theory without using any adjustable parameters. The results demonstrate agreement with molecular dynamics simulations. Thus a direct realization is presented of the key idea of statistical mechanics: for the theoretical description of the collective particle dynamics in equilibrium fluids it is sufficient to know the interparticle interaction potential and the structural characteristics. Comparison with alternative or complementary theoretical approaches is provided.

Martian hydrothermal fluids recorded in the Sm-Nd isotopic systematics of apatite in regolith breccia meteorites

The observations of Martian orbiters and rovers have suggested that there were fluids on the surface of early Mars. However, the geochemical properties of those fluids are unclear. The Martian regolith breccia meteorites (MRB), the source materials of which are thought to have formed at 4.4 Ga, may have recorded interactions with fluids on Mars. Here, we have analyzed the in situ Sm-Nd isotopic compositions and trace element contents of apatite in MRB and have obtained a Sm-Nd isochron age of 1490±480 Ma. This young age indicates that the MRB apatites were altered by fluids and have exchanged trace elements with fluids. The very negative initial ε143Nd, combined with the previously reported positive δD and δ37Cl in the MRB apatites, indicate that Martian fluids originated from a geochemically enriched reservoir in the crust. The large ranges of rare earth element abundance (ΣREE) and of the chondrite normalized ratio of La and Yb [(La/Yb)N] indicate the chemical complexity of the fluids that interacted with the apatites in the MRB. The apatite REE compositions were used to further determine the pH values of Martian fluids equilibrated with the MRB apatites, which varied from ∼3 to ∼8. The apatite X-site Cl contents indicate that the Cl contents in Martian fluids in equilibrium with the MRB apatites at 400°C and 1 bar could be up to 1857 ppm, within the range of terrestrial hydrothermal fluids. Combined with previously reported geochemical data from Martian meteorites, our study suggests that fluids may have been present throughout the early geological history of Mars.

Beltrami–Bernoulli equilibria in weakly rotating self-gravitating fluid

In the presence of a stationary gravitomagnetic field, a weakly rotating self-gravitating fluid relaxes into equilibrium flow configurations which admit both large- and small-scale structures. Unlike the traditional Beltrami equilibria in fluid, the equilibrium states in a rotating self-gravitating fluid in a gravitomagnetic field have structure similar to that of double curl Beltrami equilibria in plasma where the generalized vortical lines are aligned with the flow field. Different equilibrium flow configurations in the rotating fluid can be distinguished by the ratio between total energy and helicity. However, these fluid equilibria do not exhibit diamagnetic behaviours as observed in multi-species plasma equilibria.

An exotic microstructured globular state formed by a single multiblock copolymer chain.

In this work, we studied the equilibrium structures formed by a single (AB)k multiblock copolymer chain. Within our model, the interactions between the A-type beads were repulsive and the B-type beads could form pairwise reversible bonds with each other (BB-bonds). Our goal was to investigate how the formation of pairwise reversible bonds between the A-type beads and the B-type beads (AB-bonds) affected the structure of the chain. We observed the formation of well-studied intramolecular micelles when the AB-bonds were absent; however, the chain folding changed dramatically when the formation of the AB-bonds was introduced. In this case, the multiblock copolymer formed a globule, which had a unique heterogeneous checkerboard-like distribution of the contact density. We discovered that contacts of beads of different types (i.e., AB-contacts) occurred much more frequently than contacts of beads of the same type (i.e., AA- and BB-contacts) in these structures. This effect can be explained by a simple model of chemical equilibrium in a two-component fluid of reversibly interacting particles, which can be solved exactly. This novel type of folding can serve as a basic model for any (AB)k multiblock copolymer chain with a non-vanishing attraction between A and B blocks.

A new model for the formation of nephrite deposits: A case study of the Chuncheon nephrite deposit, South Korea

The Chuncheon nephrite deposit is the largest in South Korea with an estimated reserve of 300,000 tons. Located in mid-eastern South Korea, the deposit is in the form of lenses in the contact zone between dolomitic marble and amphibole schist in the upper part of a biotite schist. To date, the origin, process of formation, and age of the Chuncheon nephrite deposit remain unclear, which hinders our further understanding of the formation of nephrite. This study involved petrography, chemical analyses, and nephrite age determinations using optical mineralogy, electron microprobe-analyses (EMPA), X-ray fluorescence spectroscopy (XRF), and SHRIMP (Sensitive High-Resolution Ion MicroProbe) analyses of zircon. Petrographic studies indicated that the Chuncheon nephrite consists mainly of tremolite. The low contents of Cr (2.15–4.74 ppm) and Ni (2.95–4.90 ppm) are typical of dolomite-related nephrites and lower than in serpentine-related nephrites. The total REE contents are <18.5 ppm. The REE chondrite-normalized patterns display right-leaning LREE and almost flat HREE patterns, which are consistent with the REE model of dolomitic marble. The δ18O isotope compositions of the zircons (6.34‰–12.5‰) from the nephrite overlap those of the Chuncheon dolomite (2.4‰–18.2‰), indicates clearly that dolomite played an important role in the formation of the Chuncheon nephrite. The petrography and geochemistry suggest that it had a metasomatic origin involving the reactions dolomitic marble → diopside, diopside → tremolite, and tremolite → chlorite. The δD and δ18O isotope compositions of our specimens of nephrite (δD = − 95.3‰ to − 78.3‰ and − 118‰ to − 105‰; 18O = − 9.9‰ to − 7.9‰) and the hydrothermal fluids in equilibrium with the nephrite (δD = − 73.6‰ to − 56.6‰ and − 96.3‰ to − 83.3‰, 330–450 °C; δ18O = − 9.41‰ to − 6.38‰, 330–430 °C) suggest that the hydrothermal fluids were predominantly meteoric water. The zircons contain almost no mineral inclusions, which is quite different from zircons in other nephrite deposits. The variable SHRIMP U–Pb ages of the zircons (908.9 ± 4.8 to 459.1 ± 1.9 Ma (n = 7), 436.3 ± 16.9 to 359.5 ± 6.4 Ma (n = 5), and 249.9 ± 5.2 to 79.4 ± 1.9 Ma (n = 5)) in the Chuncheon nephrite may record the ages of a regional multi-stage metamorphism. Due to the generally low temperature of formation of the nephrite, we speculate that the ages of zircons only record the two relatively high-temperature initial stages of nephrite formation (dolomitic marble → diopside, and diopside → coarse-grained tremolite) and failed to record the age of the lowest-temperature third stage of high-quality nephrite formation (coarse-grained tremolite → fine-grained tremolite). It has generally been considered that dolomite-related nephrite forms at the contacts between granite/granodiorite and dolomitic marble, whereas serpentinite-related nephrite forms at the contacts between serpentinite and silica-rich rocks. However, the genesis of the Chuncheon nephrite deposit does not fit with either of these well-known types. Thus, we developed a new model for the Chuncheon nephrite in which heat was provided by regional multi-stage metamorphism, meteoric water dominated the nephrite-forming fluids, and dolomitic marble and biotite schist provided the material for the nephrite.

Low-δ18O Neoarchean precipitation recorded in a 2.67 Ga magmatic-hydrothermal system of the Keivy granitic complex, Russia

The modern hydrological cycle includes precipitation of 18O-depleted meteoric water over continental crust exposed above sea-level. How far back in the geological record can continental exposure be documented remains uncertain, particularly for the Archean. To investigate the extent of Archean continental exposure, we document a newly discovered low-δ18O magmatic-hydrothermal system that was emplaced in a shallow crust of the Keivy complex, Kola craton at 2.67 Ga. This study builds a case for syn-emplacement hydrothermal exchange with the local meteoric water that had δ18O at least as low as −11‰ VSMOW. Coupled with the high-latitude position of the Kola craton at the time, this result presents a paleogeographic documentation of continental exposure and a quantitative estimate of the isotope composition of Neoarchean precipitation. We employ detailed δ18O mapping using mineral separates and bulk samples, as well as ion microprobe δ18O measurements and U-Pb dating of zircon. The spatially extensive O-isotope dataset (n = 63) spans over 120 km in length across different lithological units including the peralkaline granites of the Keivy complex, the hosting gneiss and contact hydrothermal quartzolites. All analyzed samples, including whole rock samples and mineral separates, show δ18O below those expected for mantle- and crust-derived magmas. The lowest δ18O of ca. −7‰ are measured in minerals and bulk rock of the altered gneisses near the intrusive contacts. Peralkaline granites returned δ18O values ranging between −6 and +5‰. Zircon crystals with preserved igneous zoning have low δ18O = +2.2‰ and yield an emplacement age for the magmatic complex of 2672 ± 7 Ma. Zircon dating from quartzolites at the contact between granites and country gneisses points to fluid-rock interaction at 2.67 and at 1.77–1.79 Ga. We propose that the spatially extensive O-isotope depletion documents a Neoarchean shallow magmatic-hydrothermal system where magmatic assimilation produced the low-δ18O granites and the hydrothermal cycling of meteoric water in the ambient crust resulted in formation of low-δ18O altered host rocks. Since the lowest δ18O value measured in a rock is ca. −7‰, the equilibrium fluids had δ18O of around −9‰ under hydrothermal conditions (300-400°C) characteristic for the shallow crust around cooling intrusions. Considering that hydrothermal fluids are shifted 1-2‰ towards higher values, the contemporaneous precipitation had δ18O = −11‰ or lower. Consequently, the 2.67 Ga Keivy complex is the earliest known intact low-δ18O magmatic-hydrothermal system offering a quantitative record of the Neoarchean precipitation that can be used as a tool in paleogeographic reconstructions.

Analyses of Multiphysical Model of Electromagnetic and Fluid in Thermodynamic Equilibrium and Chemical Nonequilibrium State

During the flight of a hypersonic vehicle, a plasma sheath will be produced around the vehicle due to the effect of the shock layer. Because the plasma sheath will absorb, reflect, and scatter electromagnetic waves, which causes the communication signal to be attenuated or even interrupted, forming a communication “blackout.” In this article, the plasma sheath is illuminated by a high-power microwave (HPM) when the hypersonic vehicle is in the state of thermodynamic equilibrium and chemical nonequilibrium. Thus, the parameters of the plasma sheath change because of absorbing the energy of the HPM and then affect the electromagnetic characteristics of the plasma sheath. Aiming at the interaction between the HPM and the plasma sheath, we propose a multiphysics coupling model of fluid field and electromagnetic field, which provides a way of thinking for the interaction of electromagnetic and fluid coupling. Furthermore, through this multiphysics coupling method, it is found that the HPM illuminates into the plasma sheath, the ability of low-frequency electromagnetic waves to pass through the plasma sheath will be improved within a specific time window, which provides a possibility to enhance the communication blackout problem. Since the primary purpose of this article is to reveal the multiphysics field method and its related phenomena, both theoretical derivations and numerical examples are only presented in the 2-D space.

Analysis of pH and electrolytes in blood and ruminal fluid, including kidney function tests, in sheep undergoing long-term surgical procedures

BackgroundThe physiology of sheep as small ruminants is remarkably different from monogastric animals especially regarding the forestomach system. Using sheep for surgical procedures during scientific research thereby presents an exceptional setting for the anaesthetist. Long-term anaesthesia generally demands deprivation of food to reduce the risk of bloat in sheep. This might influence the energy and electrolyte balance. In horses and companion animals, close monitoring of mean arterial blood pressure, capnography and blood gas analysis are common procedures during long-term surgery. However, few data are available on reference ranges for blood gas in sheep and these cover only short periods of anaesthesia. To the authors’ knowledge, there is no study available that includes the monitoring of electrolytes and pH in ruminal fluid and kidney function tests in sheep undergoing long term anaesthesia. Thereby, the aim of the present study was to gather data on blood parameters, and data on ruminal fluid and kidney function during long-term anaesthesia in sheep. Data were obtained from eight sheep undergoing the invasive surgical procedure of left pneumonectomy and auto-transplantation or isolated left lung perfusion. After a 19-h fasting period, the animals were administered xylazine and ketamine and then intubated and maintained in general anaesthesia under artificial ventilation using isoflurane in oxygen. Blood samples were evaluated during 9 h of anaesthesia; ruminal fluid and kidney function tests were evaluated during 7 h of anaesthesia.ResultsBlood parameters such as electrolytes and partial pressure of carbon dioxide revealed few changes, yet blood glucose decreased and beta-hydroxybutyric acid increased significantly. All animals showed an elevated arterial pH and bicarbonate concentration despite artificial ventilation. In ruminal fluid, the pH significantly decreased and no significant changes in electrolytes occurred. Kidney function tests revealed no significant changes in any of the animals. However, fractional excretion of water and phosphate was slightly increased. One animal showed severe complications due to hypokalaemia.ConclusionInvasive surgery under long-term anaesthesia in sheep is possible without great imbalances of arterial pH and electrolytes. Nevertheless, potassium concentrations should be monitored carefully, as a deficiency can lead to life-threatening complications. The operated sheep tended not to develop metabolic acidosis and the mean kidney function could be maintained within the physiological range throughout anaesthesia. However, slight elevations in renal fractional water and phosphate excretion could suggest an early tubular reabsorption dysfunction. In ruminal fluid, acidification occurred, though no significant changes were observed in l- and d-lactate levels or in electrolyte concentrations. To our knowledge, the role of the rumen in storing fluids and balancing electrolytes in the blood has not yet been documented during anaesthesia. However, the importance of the rumen for fluid equilibrium in sheep indicates the necessity for routine monitoring and further research.

Experimental investigation of the effect of nitrogen on the phase equilibrium behavior of the CH4–CO2 mixture at low temperature for natural and biogas purification

New fluid-fluid and solid-fluid(-fluid) equilibrium measurements at 4 MPa for the N 2 + CH 4 + CO 2 system have been carried out using a static-analytic method in order to investigate the effect of nitrogen on the phase equilibrium behavior of the methane + carbon dioxide mixture at temperatures between 170 K and 210 K. With respect to equilibria involving solid carbon dioxide, the addition of nitrogen to the mixture reduces the solubility of carbon dioxide in the fluid phase, widens the temperature region of existence of the solid-vapor equilibrium, and spreads the temperature range of existence of the solid-liquid-vapor equilibrium. The comparison between measured values and values calculated by means of the Peng-Robinson Equation of State as implemented in Aspen HYSYS® shows that tabulated binary interaction parameters (regressed with respect to fluid-fluid equilibria) are not always suitable when applied to the calculation of low temperature equilibria.